What is the correct formula for calculating capacitance of a capacitor?

The correct formula for calculating capacitance of a capacitor is represented accurately by the relationship involving the permittivity of free space, the dielectric constant, the area of the plates, and the distance between them. Specifically, capacitance ( C ) can be expressed as:

[ C = \epsilon_r \cdot \epsilon_0 \cdot \frac{A}{d} ]

where:

• ( \epsilon_0 ) is the permittivity of free space (approximately ( 8.85 \times 10^{-12} , F/m )),

• ( \epsilon_r ) is the relative permittivity or dielectric constant ( k ),

• ( A ) is the area of one of the plates, and

• ( d ) is the distance between the plates.

This formula illustrates that the capacitance of a capacitor depends directly on the size of the plates (area) and inversely on the distance between them. As the area increases, capacitance increases, and as the distance increases, capacitance decreases. This fundamental understanding is crucial for designing capacitors in circuits where specific capacitance is required.

The other options provided do not accurately represent the formula for capacitance. For instance, the